Abstract
This article proposes a rational fractal interpolation function (FIF) with three families of shape parameters based on function values only. The proposed FIF involves rational functions with numerators as cubic polynomials chosen according to the interpolation conditions and denominators as preassigned quadratic polynomials with three shape parameters. An upper bound for the error in the uniform norm for the rational cubic FIF is expressed in terms of analogous interpolation error bounds for its classical counterpart and the convergence is deduced. The parameters involved in the rational fractal functions are identified so as to solve certain constrained interpolation problems. We illustrate our interpolation scheme with some numerical examples.
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